Abstract

Corners in surface markings are skewed by orthographic projection into an image. This introduces a systematic bias into the distribution of corner angles in images. Under the assumption that all corner angles in surface markings are equally probable, the distribution of corresponding angles in contour corners shows a peak probability of occurrence at 0° and 180° and a minimum at 90°. The exact form of the distribution depends on the assumed distribution of surface orientations in scenes. The bias allows us to derive a maximum likelihood estimator of surface orientation from the information provided by contour corner angles without making any assumptions about the distribution of surface marking corners in scenes. The estimator performs in a manner consistent with human perception in the interpretation of simple line figures. In particular, simple corners lead to an estimate of surface orientation consistent with the corners having been projected from 90°, and skewed symmetries lead to estimates consistent with the figures having been projected from real symmetries. As examples of the latter, triangles are interpreted as oriented isosceles triangles and skewed rectangles are interpreted as oriented rectangles. Though the estimator does not rely on any regularity assumptions for surface markings, incorporation of such constraints would make the estimator more resistant to noise.

© 1992 Optical Society of America